What you really want with a categorization scheme is to reduce variance. You ask, "how much variance reduction do I see using this categorization scheme?" This could be expressed as a percentage of total variance, like "U.S. Census 5-races captures 27% of variance".
Race is real. U.S. race categories are not the same as used elsewhere in the world. U.S. Census categories map quite well to genetics. They capture a lot of variance. Ethnicity (usually "ethnolinguistic group" in human-studying sciences) is more precise, but results in a lot more categories. You can capture all the variance with infinite categories. This is the bias-variance tradeoff. This is how things are.
Race is real. U.S. race categories are not the same as used elsewhere in the world. U.S. Census categories map quite well to genetics. They capture a lot of variance. Ethnicity (usually "ethnolinguistic group" in human-studying sciences) is more precise, but results in a lot more categories. You can capture all the variance with infinite categories. This is the bias-variance tradeoff. This is how things are.